The Class-D Amplifier(课程教材)

The Class-D Amplifier(From the book Introduction to Electroacoustics and Audio Amplifier Design,Second Edition-Revised Printing,by W.Marshall Leach,Jr.,published by Kendall/Hunt, c°2001.)A class-D amplifier is one in which the output transistors are operated as switches.When a transistor is off,the current through it is zero.When it is on,the voltage across it is small,ideally zero.In each case,the power dissipation is very low.This increases the efficiency,thus requiring less power from the power supply and smaller heat sinks for the amplifier.These are important advantages in portable battery-powered equipment.The“D”in class-D is sometimes said to stand for“digital.”This is not correct because the operation of the class-D amplifier is based on analog principles.There is no digital coding of the signal.Before the advent of the class-D amplifier,the standard classes were class-A,class-AB,class-B,and class-C.The“D”is simply the next letter in the alphabet after“C.”Indeed,the earliest work on class-D amplifiers involved vacuum tubes and can be traced to the early1950s.Fig.1shows the basic simplified circuit of a class-D amplifier.We assume a bipolar power supply so that V−=−V+.The amplifier consists of a comparator driving two MOSFET transistors which operate as switches.The comparator has two inputs.One is a triangle wave,the other is the audio signal.The frequency of the triangle wave must be much higher than that of the audio input.The voltage output of the comparator can be writtenv C=−V1for v S>v T v C=+V1for v S<v T(1)This voltage is applied to the input of a complementary common-source MOSFET output stage. Each transistor operates as a switch.For v C=−V1,M1is on and M2is off.If the voltage drop across M1is negligible,then v0O=V+.Similarly,for v C=+V1,M2is on,M1is off,and v0O=V−. In practice,there is a small voltage drop across the on MOSFET switch so that the peak output voltage is less than the power supply voltage.For the case v S=0,v0O is a symmetrical square wave.The low-passfilter consisting of L1and C1passes the average value of the square wave to the loudspeaker,which is zero.Thus v O=0for v S=0.The network consisting of R1and C2compensates for the inductive impedance of the loudspeaker voice coil so that thefilter sees a resistive load at high frequencies.Figure1:Basic class-D amplifier.Fig.2shows the circuit waveforms for the case where v S is a sine wave.For purposes of illustration,the sine wave frequency is f S=1kHz and the triangle wave frequency is f T=20kHz. The sine wave amplitude is0.75V T P.For v S>0,the duty cycle of the square wave changes so that v0O spends more time at its positive level than at its negative level.This causes v0O to have a positive average value.Similarly,for v S<0,v0O has a negative average value.The waveform for v0Ois said to be pulse-width-modulated.The passive filter consisting of L 1and C 1passes the averageor low-frequency value of v 0O to the loudspeaker load and rejects the higher-frequency harmonics ofthe switching waveform.Figure 2:Ampli fier voltage waveforms.The e ffective gain of the ampli fier can be determined by applying a dc voltage at the input andcalculating the ratio of h v 0O i to v S ,where h v 0O i denotes the low-frequency time average of v 0O .If v S is increased,h v 0O i increases linearly until it reaches the level V OP ,which corresponds to the positiveclipping voltage at the output.This occurs when v S =V T P .It follows that the e ffective gain k is given by k =h v 0O i v S =V OP V T P(2)Fig.3shows the waveforms of the output voltage v O for two values of the cuto fffrequency of the LC filter.The transfer function of the filter isV o V 0o =1(s/ωc )2+(1/Q c )(s/ωc )+1(3)where ωc =2πf c =1/√L 1C 1is the resonance frequency and Q c =1/(ωc R L C 1)is the qualityfactor.The load resistance R L is the e ffective high-frequency resistance of the loudspeaker voice coil in parallel with the matching network consisting of R 1and C 2.The quality factor is Q c =1/√2for the waveforms in Fig.3so that the gain is down by 3dB at ωc .The signal frequency is f S =1kHz.The filter resonance frequency for the v O 1waveform is f c =1kHz.For the v O 2waveform,it is f c =8kHz.The harmonics of the pulse-width-modulated signal are clearly visible on the v O 2waveform.For minimum distortion,the frequency of the triangle wave should be as high as possible compared to the cuto fffrequency of the filter.Because the filter resonance frequency corresponds to the signal frequency for the v O 1waveform in Fig.3,the phase lag is 90o .The phase lag for the v O 2waveform is less because the resonance frequency is greater than the signal frequency.A higher-order filter can be used to more e ffectively remove the high-frequency switching harmonics.For example,a third-order LC filter or a fourth-order filter consisting of the cascade of two second-order LC filters could be used.Fig.4shows the spectrum of the v 0O waveform.It contains a fundamental at f S .Above f S ,the signi ficant switching harmonics are at f T ,f T ±2f S ,2f T ±f S ,2f T ±3f S ,etc.The lowest of these is at the frequency f T −2f S .The triangle wave frequency must be chosen high enough soFigure3:Output voltage waveforms for two different LCfilter cutofffrequencies.that the lowest significant harmonic is well above the highest signal frequency of interest.Thus we have the requirement f T−2f SÀf S or f TÀ3f S.To minimize ripple on the output,the cutofffrequency of the LCfilter should be much lower than f T.For example,in a wideband amplifier with a maximum signal frequency of20kHz,the switching frequency should ideally be600kHz or greater.Because of limitations imposed by a high switching frequency,a more practical value might be300kHz.The−3dB frequency of the LCfilter should be much lower than the switching frequency.For example,it might be30kHz for a300kHz switching frequency.Note that the amplitude of the harmonic at f T is larger than that of the signal.At the signal clipping level,the signal harmonic becomes1.5times as large as the harmonic at f T.Figure4:Unfiltered spectrum of the output voltage.Negative feedback can be used around the basic amplifier circuit to improve its performance. Fig.5shows such a circuit.The input op amp acts as an integrator to set the bandwidth.For a sinusoidal input signal with a frequency much lower than the switching frequency,the effective transfer function for the circuit and its pole frequency are given byV0o V s =−R FR211+s/ω0ω0=2πf0=kR F C F(4)The pole frequency must be greater than the highest frequency to amplified but lower than the switching frequency.Because the integrator has a very high gain at dc,it acts to minimize dc offsets at the output.For a wide band amplifier,a typical value of f0might be60kHz.Class-D amplifiers are often operated in a bridged configuration to increase the output power without increasing the power supply voltages.A bridged output stage is shown in Fig.6.A typical input circuit is shown in Fig.7.The feedback voltage v F is proportional to the difference voltageFigure5:Amplifier with negative feedback.v0O1−v0O2.The bridge circuit is often designed with V−=0and a dc offset at each output of V+/2 V,thus eliminating the need for a bipolar power supply.Figure6:Bridged output stage.Figure7:Input stage to the bridged amplifier with feedback.In the circuit of Fig.7,a diffamp is used to subtract v0O2from v0O1.The capacitors labeled C3 act as low-passfilters to limit the rise time of the signals applied to the op amp to prevent slewing. The transfer function for the diffamp and its pole frequency are given byV fV0o1−V0o2=R5R3+R411+s/ω1ω1=2πf1=1(R3k R4)C3(5)The overall transfer function for the amplifier is given byV0o1−V0o2V s =−R FR2R3+R4R51+s/ω1s/ω1ω2+s/ω2+1=−R FR2R3+R4R51+s/ω1(s/ω0)2+(1/Q0)(s/ω0)+1(6)whereω2,ω0,and Q0are given byω2=2πf2=R5R3+R4kR F C Fω0=2πf0=√ω1ω2Q0=rω2ω1(7)The amplifier should exhibit good stability for Q0≤1.Thus we have the conditionω1≥ω2. However,the simple model used here neglects higher order poles.Because the existence of such poles degrades stability,a conservative approach might be to design for Q0≤0.5so that the poles in Eq.(6)are real.This requiresω1≥4ω2.For example,in a wideband amplifier utilizing a switching frequency of300kHz,f1might be chosen to be equal to the switching frequency and f2 might be chosen to be75kHz.An example triangle wave generator circuit is shown in Fig.8.The circuit consists of an inte-grator driving a comparator that is connected as a Schmitt trigger.The output of the comparator drives the input to the integrator.Let the comparator output voltages be+V1and−V1.When the voltage is at the−V1level,the triangle wave output rises with the slope m=V1/R6C4.Let the peak values of the triangle wave be+V T P and−V T P.It follows that2V T P=mT/2=V1/2f T R6C4, where T=1/f T is the period of the triangle wave.The comparator switches states when the volt-age at its non-inverting input goes through zero.This occurs when V1/R8=V T P/R7.Solution forf T and V T P yieldsf T=R84R6R7C4V T P=R7R8V1(8)Figure8:Triangle wave generator.A problem called“shoot through”can reduce the efficiency of class-D amplifiers and lead to potential failure of the output devices.This occurs during the transition when one device is being cut offand another is being cut on.During the transition,both devices are on and a large current pulse canflow through the two.This can be eliminated by driving the gates of the MOSFETs with asymmetrical square waves such that one device is cut offbefore the other is cut on.One way of achieving this in the circuit of Figs.1and5is to use two comparators,one for each MOSFET.A positive dc offset is added to the triangle wave input to the comparator which drives M1and a negative dc offset is added to the triangle wave input to the comparator which drives M2.This effectively adds crossover distortion to the v0O output waveform,but the frequency components are above the switching frequency,thus outside the audio band.The high switching frequency used in class-D amplifiers is a potential source of rf interference with other electronic equipment.The amplifiers must be properly shielded and grounded to prevent radiation of the switching harmonics.In addition,low-passfilters must be used on all input and output leads,including the power supply leads.A variation of the class-D amplifier is called afilterless class-D amplifier.In the absence of an input signal,its output signal is zero rather than a symmetrical square wave.This eliminates the need of a low-passfilter to prevent application of the square wave to the loudspeaker.When the input voltage goes positive,the output voltage is a train of pulse width modulated pulses which switch between0and+V OP.When the input voltage goes negative,the output voltage is a train of pulse width modulated pulses which switch between0and−V OP.This is illustrated in Fig.9.The loudspeaker responds to the average value of the signal,which is the audio signal.Because there is nofilter,rf interference problems require the amplifier to be mounted as close to the loudspeaker as possible.The spectrum of the output signal is shown in Fig.10.One problem with thefilterless class-D amplifier is crossover distortion.To eliminate this,the FET control logic must be designed so that the amplifier puts out very narrow alternating positive and negative pulses in the absence of an input signal.In effect,this biases the amplifier in the class-AB mode.Figure9:Amplifier voltage waveforms.Figure10:Spectrum of the output voltage v0O.。